%Abstract
In this report we describe the background theory of how the finite element method can be used to deform bodies in a virtual environment as well as presenting how we implemented it. In more detail the mechanics of physical bodies will be brought up, like how stress and strain affects them and results in internal forces which will in turn cause deformations. We will then continue and describe how to discretize the system using the finite element method, bring up and explain the different terms necessary to give a good understanding of the problem. 

Since our goal was to achieve deformations in real time a lot of considerations was taken to linearize several problems. This did not go without the cost of artifacts, so there will be an explanation of how the warped stiffness method proposed by M\"uller and Gross \cite{muller_ivm} is used to compensate for these.